Young Tableaux

[Emeric Deutsch (RP)[M}]

Thanks Wouter. Here is the Maple worksheet for the sum.
> S:=n->sum(n!/k!/(n-2*k)!/2^k,k=0..floor(n/2));

                         floor(1/2 n)
                            -----
                             \               n!
               S := n ->      )       ----------------
                             /                       k
                            -----     k! (n - 2 k)! 2
                            k = 0
just checking:

> seq(S(n),n=0..12);

     1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152

> simplify(S(n));

  - (-hypergeom([- 1/2 n + 1/2, - 1/2 n], [], 2)

        GAMMA(2 + floor(1/2 n)) GAMMA(n - 2 floor(1/2 n) - 1) +

                      (-1 - floor(1/2 n))
        GAMMA(n + 1) 2                    hypergeom(

        [1, - 1/2 n + floor(1/2 n) + 1, - 1/2 n + floor(1/2 n) + 3/2]

        , [2 + floor(1/2 n)], 2))/(

        GAMMA(2 + floor(1/2 n)) GAMMA(n - 2 floor(1/2 n) - 1))

Emeric